#include<iostream>
#include<vector>
#include<queue>
#include<cstring>
#include<cmath>
#include<map>
#include<set>
#include<cstdio>
#include<algorithm>
#define debug(a) cout<<#a<<"="<<a<<endl;
using namespace std;
const int maxn=1e5+1000;
typedef long long LL;
inline LL read(){LL x=0,f=1;char ch=getchar();	while (!isdigit(ch)){if (ch=='-') f=-1;ch=getchar();}while (isdigit(ch)){x=x*10+ch-48;ch=getchar();}
return x*f;}
LL a[maxn];
int main(void){
   	cin.tie(0);std::ios::sync_with_stdio(false);
    LL t;cin>>t;
    while(t--){
        LL n;cin>>n;
        for(LL i=1;i<=n;i++){
            cin>>a[i];
        }
        if(n%2==0){
            cout<<"YES"<<endl;
        }
        else{
            bool flag=false;
            for(int i=1;i<n;i++){
                if(a[i]>=a[i+1]) flag=true;
            }
            if(flag) cout<<"YES"<<endl;
            else cout<<"NO"<<endl;
        }
    }
   	return 0;
}
